Active Structural Control: Theory and Practice (Longman structural engineering & structural mechanics series)

Active Structural Control: Theory and Practice TT Soong Department of Civil Engineering State University of New York at Buffalo Advisory Editor W F Chen School of Civil Engineering Purdue University

Longman Scientific & IIIIUIIIIIII Te h . l

... 11111 ... 11111111111111

-

C nlCQ

Copublished in lhe United States with John Wiley & Sons, lm::., New York

Longman Scientific & Technical Longman Group UK Limited, Longman House, Burnt Mill. Harlow, Essex CM:ZO :ZJE, England and Associated Companies throualwul the world. Copublished in the United States witlz Jolm Wiley & Sons, Inc .. 60j Third Avenue, New York, NY 10158

(CJ Longmun Group UK Limited

1990

All rights reserved; no part of this publication may be reproduced, stored in u retrieval system, or transmitted in any form or by any means, electronic, mechanical. photocopying, recording, or otherwise without either the prior written permission of the Publishers or a licence permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, 33~34 Alfred Place, London, WCIE 7DP. First published 1990 British Library Cataloguing in Publication Data Soong. T. T. Active structural control. 1. Structures.Control I. Title 624.1

ISBN 0-582-01782-3 Library of Congress Cataloging-in-Publication Datil Soong, T. T. Active structural control : theory and practice/ T.T. Soong; advisory editor, W. Chen. em. p. Includes bibliographical references. ISBN 0-470-21670-0 L Structural engineering. 2. Control theory. I. Title. 1990 TA630.S66 89-13859 624.1'771--dc20

CIP Typeset in 10/12 pt Monotypc Times Roman Printed and Bound in Great Brituin at the Bath Press. Avon

To Professor John L Bogdanoff Teacher, Mentor, and Friend

Contents

Preface

ix

Acknowledgements

Xl

1 Introduction l 1.1 Organization 3 References 4 2

Actively controlled structures References 8

5

3 Control algorithms 10 3.1 Classical linear optimal control 11 3.2 Pole assignment 28 3.3 Instantaneous optimal control 36 3.4 Independent modal space control (IMSC) 3.5 Bounded state control 49 3.6 Other control algorithms 57 References 57 4

Practical considerations 60 4.1 Modelling errors and spillover effects 60 4.2 Time delay 68 4.3 Structural nonlinearities 73 4.4 Uncertainties in structural parameters 86 4.5 Limited number of sensors and controllers 4.6 Discrete time control 97 4.7 Reliability 110 4.8 Other considerations 112 References 113

5 Control mechanisms and experimental studies 5.1 Active tendon control 116

45

89

116

vii

Contents

5.2 5.3 5.4 5.5

Active mass damper and active mass driver Pulse generators 146 Aerodynamic appendages 150 Other control mechanisms !54 References 155

6 Optimization of actively controlled structures 6.1 Basic equations 164 6.2 Solution procedure 166 References 175 Appendix A: Elements oflinear control systems A.! The state equation 177 A.2 Solution of the state equation 181 A.3 Stability 186 A.4 Controllability and observability 189 Bibliography 190 Appendix B: Conversion table Subject index

viii

193

192

136

159

177

Preface

Natural hazard mitigation is one of the most important issues facing civil engineers today. Many of us have experienced the feeling of helplessness when our homes or offices were shaken uncontrollably by earth tremors. All of us have witnessed through television and other news media the vast destruction of properties and tragic loss of lives caused by an earthquake, a hurricane, a fire or a flood. In structural engineering. one of the constant challenges is to find new and better means of protecting structures and constructed facilities from the damaging etTects of destruc;tive environmental forces. One avenue open to the researchers and designers is to introduce more conservative designs so that structures such as buildings and bridges are better able to cope with large external loads. This approach, however, can be untenable both technologically and economically. Another possible approach is to make structures behave more like machines, aircrafts, or human beings in the sense that they can be made adaptive or responsive to external forces. Structural muscles, so to speak, can be flexed when warranted, or appropriate adjustmen}s can be made within the structure as environmental conditions change. This latter approach has led to active structural control research and has opened up a new field of investigation. which began more as an intellectual curiosity in the early 1970s but now is at the stage where large-scale experimentation is underway and actual active control systems have been designed and installed in full-scale structures. Another reason that active structural control has been receiving an increasing amount of attention has to do with rapid advances that have been taking place in allied technologies. The development of the active control concept must go hand-in-hand with advances in areas such as computers, electronics. measurement techniques, instrumentation, controllers. actuators, materials, etc. Current phenomenal advances in all these areas have given added impetus to the development of active control technology. They also reflect favourably on the all-important cost factor. On the basis of the analytical and experimental results obtained to date, it appears evident that, technologically, fully automated active systems are within sight of becoming a reality. At the same time, however, a large number of serious obstacles remain and they must be overcome before active structural ix

Preface

control can gain general acceptance by the civil engineering and construction professions at large. This brings us to the purpose of writing this book. It is intended to introduce to the interested reader basic principles involved in the theory o[ active structural control, to bring together in one volume a wealth of information documenting progress that has been made to date, and to address implementational issues. It is hoped that the material in this book will provide the reader with some added degree o[ understanding and maturity so that he or she may better delineate imponant issues involved and pursue further studies in this exciting and fast expanding field. T T Soong Buffalo, New York August, 1989

X

Acknowledgements

My work in this research area has been supported since 1976 by the National Science Foundation. This continuing support is gratefully acknowledged. Since 1986, funding for my active control research has been shared by the National Science Foundation and the State of New York under the auspices of the National Center for Earthquake Engineering Research. I am also grateful to NATO, US-Spain Joint Committee for Science and Technological Cooperation. and Humboldt Foundation for their generous support of this work. This book first took shape when I was associated with the Curt-Risch· lnstitut, University of Hannover, under the Humboldt Foundation Senior US Scientist Award Program. Industrial participation and contributions were also important to the success of this research effort, particularly during the large-scale experimental phase. It is a pleasure to acknowledge support received from the MTS Systems Corporation, the Takenaka Corporation of Japan and Kayaba Industry Ltd of Japan. I am indebted to many of my colleagues with whom I have collaborated over many years. Professor James T P Yao of Texas A&M University introduced me to this research topic and provided invaluable guidance throughout. Professor A M Reinhorn has been my close associate at the State University of New York at Buffalo and has made invaluable contributions to our joint research programs. Professors J Rodellar and A H Barba! of the Technical University of Catalunya were kind enough to review earlier drafts of this book and made improvements. I have also learned a great deal about active control from the late Professor H H E Leipholz of the University of Waterloo and from Professor J N Yang of the George Washington University. I have also had the good fortune of working with some of the most talented students on various active control projects. A vote of sincere thanks to C Martin, L L Chung, Z Prucz, R C Lin and S McGreevy. My sincere thanks also go to my secretary, Mrs Cannella Gosden, who expertly and unflinchingly typed hundreds of pages of text and equations, and uncomplainingly made revision after revision. Finally, I owe a special debt of gratitude to my wife, Dottie, who, for the fourth time, endured with good humour and provided unwavering support to this writing project. xi

Acknowledgements

We are indebted to the following for permission to reproduce copyright material: American Society of Civil Engineering for llgs 3.1 & 3.18-3.22 from figs l, 2, 3, 6, 7, 11 (Yang, Akbarpour & Ghaemmaghami, 1987), figs 3.2, 3.5-3.7 & 4.6 from figs !, 2 & 6-8 (Chung, Reinhorn & Soong, 1988), figs 3.8-3.12 from figs 2 & 5-8 (Yang, 197 5), figs 3.13 & 3.!4 from figs 3 & 4 (Martin & Soong, 1976), fig. 4.5 from fig. 5 (Pu, 1989 ), figs 4.22 & 4.23 from figs 1 & 2 (Pantelides & Cheng, 1989), figs 5.2-5.4 from figs 1 & 2 (Reinhorn & Soong, 1989), fig. 5.24 from fig. 3(a) (Yang, 1982), fig. 5.28a& b from figs 12 & 13 (Miller, Masri, Dehghanyar & Caughey, 1988), figs 5.32 & 5.33 from figs 5 & 6 (Soong & Skinner, 1981 ), figs 6.1-6.4 from figs l-4 (Soong & Manolis, 1987) and figs 6.5-6.12 from figs 2-9 (Cha, Pitarresi & Soong, 1988): American Society of Mechanical Engineers for figs 3.24, 3.25, 3.27, 3.29 & 3.30 from figs 1·-5 (Prucz, Soong & Reinhorn, 1985); Butterworth Scientific Ltd. and the author, Professor F Kozin for figs 3.15-3.17 from figs 2 & 4 (Wang, Kozin & Amini, 1983); Kajima Corporation for figs 5.22a& b, 5.26a& b & 5.27; E & F N Spon for fig. 4.33 from fig. 3 (Basharklah & Yao, 1984); Takaneka Corporation for figs 5.16, 5. 19a & b and 5.25a & b; one of the authors, Professor S F Masri for figs 5.29, 5.30 & 5.31 from pp. 447-52 (Traina et aL 1988).

xii

1

Introduction

It is common knowledge that civil engineering structures must wi[hstand environmental loads, such as wind, earthquakes and waves, over the span of their useful lives. Yet, until very recently, buildings, bridges, and other constructed facilities have been built as passive structures that rely on their mass and soli.dity to resist outside forces, while being incapable of adapting to the dynamics of an ever-changing environment. Indeed, 'solidity' and 'massiveness' have often been equated to 'safety' and 'reliability'. In recent years.- however, a number of factors have emerged that signal the need for considering structures with some degree of adaptability or responsiveness. These factors include the following:

ever~changing

Increased flexibility: With the trend towards taller. longer and more flexible structures, undesirable vibrational levels could be reached under large environmental loads, thus adversely affecting human comfort and even structural safety. 2 Increased safety levels: Higher safety levels are demanded as structures

become more complex, more

3

costly~ an~

serve more critical functions.

Examples are tall structures, deep-water offshore platforms, and nuclear power plants. In these cases, conventional reliability criteria are no longer adequate and failure is synonymous with disaster. lncreasiuuly stringent pe({ormance requirements: Within safety limits, conventional structures are allmved to deform and even sustain local damage if necessary. Structures are increasingly required, however, to

operate within strict performance guidelines such as alignment or shape constraints. Examples in this area are radar tracking stations, radio

telescope 4

structures~

and aerospace structures.

Better ltti/i:::ation of material and haver cost: Partly due to the considerations just given, and partly due to economic consideration, it is clear that savings in materials, weight; and cost are not only desirable but necessary. This is especially true for structures in space and for portable structures used in military applications.

As a result, new concepts of structural protection and structural motion control, such as supplemental damping, passive control and active control,

Aclive structural control: theory and practice

have been advanced and are at various stages of development. In the area of passive systems, they include base isolation systems against earthquake loads, tuned mass dampers and fluid sloshing damper systems against wind, and a variety of mechanical energy dissipaters such as bracing systems, friction dampers, viscoelastic dampers and other mechanical dampers. In the active system area, active mass dampers, active mass drivers, active tendon systems, pulse thrusters, and active variable stiffness systems are some of the devices being developed and tested both in the laboratory, and in some cases, in actual structural applications. The operating principle of a passive protective system is now adequately understood; less so, however, for active systems. In structural engineering, 'active structural control' has become known as an area of research in which the motion of a structure is controlled or modified by means of the action of a control system through some external energy supply. Active systems are presently under close scrutiny in terms of their future structural applicability stemming from a number of motivating factors. They include the following: As mentioned earlier, with the advent of new materials and new construction methods, structures are becoming taller, longer and more flexible. The application of active control is one of the options in safeguarding such structures against excessive vibrations. In fact, 'supertall' buildings with up to 500 storeys are being considered as possibilities in the near future, 1 •2 for which control systems, either active or passive, may become an integral part 2 Active or hybrid active-passive systems can be attractive candidates for retrofitting or strengthening existing structures against, for example, earthquake hazards. Current passive means of using interior shear walls or base isolation systems are structurally invasive. Active systems, on the other hand, can be more effective and can be incorporated into an existing structure with less interference. In a report prepared for the National Research Council addressing research issues based on lessons learned from the 1985 Mexico earthquake,' research on retrofit of buildings using devices which 'might increase damping or modify the natural period' is recommended. This objective can be easily achieved using active or active-passive systems. 3 Civil engineering structures are not designed to withstand all possible external loads. However, extraordinary loading episodes do occur, resulting in structural damage or even failure. Active control in this context can mean a last resort attempt to save a structure which, without it, would not be able to survive. This extra protection is particularly attractive when one considers the high cost of some recent large structures such as deep-water offshore platforms, not even mentioning lives that might be lost otherwise. The same is true for structures which serve critical functions such as hospitals and nuclear power plants. 1

2

Intruducduu

4 Some structures house valuable and sensitive equipment or secondary systems. Their operating safety is of paramount importance. Active control can thus be applied at the substructure level to ensure proper operating conditions for secondary systems. 5 Passive control devices such as base isolation systems, viscoelastic dampers and tuned mass dampers, have been installed in some existing structures, resulting in improved structural performance. Passive devices, however, have inherent limitations. Consider, for example, the tuned mass damper system installed in the Citicorp Center, New York. 4 • 5 • 6 Since it is tuned to the first modal frequency of the structure, it is basically designed to reduce only the 6rst mode vibration. An active mass damper, on the other hand, can be effective over a much wider frequency range, Hence, the study of active structural control is a logical extension of passive control technology, 6 Finally, the idea of active control itself is not only attractive, but potentially revolutionary, since it elevates structural concepts from a static and passive level to one of dynamism and adaptability. One can envisage future structures having two types of load resisting members: the traditional passive members that are designed to support basic design loads, and active members whose function is to augment the structure's capability in resisting extraordinary loads. Their integration in an optimal fashion can conceivably result in better utilization of material and lower cost 7 - 9

Thus motivated, there has been a flurry of research activities in the area of active control of civil engineering structures over the last 20 years. In this book, an attempt is made to provide the reader with a working knowledge of this exciting and fast expanding field. Moreover, current research and development work in active control is brought up-to-date as much as possible,

1.1

Organization

The material of this book flows from theoretical background to practical considerations to implementational'issues. Chapters 2 and 3 are concerned with the fundamental principles of active structural control and with the development of control algorithms suitable for structural control applications. Topics in these chapters are better understood when the reader has a working knowledge of elementary structural dynamics, random vibration, systems theory and control theory. Of the above knowledge areas, theoretical aspects of systems and control theory may not be familiar to some of the readers. Consequently, a brief introduction and a summary of results in linear control systems are given in Appendix A, together with a list of useful references. 3

Acth·e structural control: theory and practice

Chapter 4 deals with practical considerations in control implementation. Issues addressed in this chapter include modelling errors, time delay in control execution, inelastic structural behaviour, and problems arising from hardware and computational limitations. As mentioned earlier, several control devices are being actively considered for structural applications. In fact, large-scale testing is underway for some active structural control systems and, at least in one case, full-scale structural implementation has taken place. Discussions in Chapter 5 centre around some of these feasible control schemes with emphasis on their performance in the laboratory. Actively controlled structures are a new strain of structural systems and their optimization takes on an added dimension in scale as well as in complexity. In Chapter 6, this optimization problem is addressed from one particular point of view. It is hoped that this brief exploration will lead to more serious investigations into many fascinating aspects of this challenging problem. Finally, it should be pointed out that, since many references were used in the development of this book, no attempt was made to unify the units of quantities used in the text and in the examples. It was felt that, to leave them in their original units, easier reference to the original publications could be made. For convenience, a conversion table for English-unit to SI-unit conversion is provided in Appendix B.

References l.

L

3.

4.

5. 6.

7. 8.

9. 4

Supertall Structures, the Sky's the Limit. Enyineerill.lJ News Record November 1983 Tucker 1 8 1985 Superskyscrapers: Aiming for 200 Storeys. High Tech 5 pp 50-63 NRC Committee on Earthquake Engineering Research A{Jenda: Learninq from the 19 September 1985 Mexico Earthquake National Research Council, Washington DC 1986 Petersen N R 1980 Design of Large Scale Tuned Mass Dampers. In Leipholz H HE (ed) Structural Control North Holland, Amsterdam pp 581~96 Tuned Mass Damper Steady Sway of Skyscraper in Wind. Engineerino News Record 28~9 August 1977 Wiesner K 8 1979 Tuned Mass Dampers to Reduce Building Wind Motion Preprint 3510 ASCE Convention Boston Soong T T and Manolis G D 1987 On Active Structures. ASCE Joumal of Structural En{filleering ll3 pp 2290-301 Soong T T and Pitarresi J M 1987 On Optimal Design of Active Structures. In Jenkins D R (ed) Compwer Applications in Structural EnrJineainy ASCE NY pp 579-91 Cha J Z, Pitarresi J M and Soong T T 1988 Optimal Design Procedures for Active Structures. ASCE Joumal of Structural Enyineerinq 114 pp 2710-23

.

2

Actively Controlled Structures

Some early notions of an actively controlled structure are contained in work

by Zuk " 2 in which the notion of'kinetic structures' is advanced. Zuk made the distinction between active controls which are designed to reduce structural motion and those which generate structural motion. The kinetic structures described by Zuk belong to the latter. Conceptually, Zuk visualizes all manner of buildings as being able to change form, shape, and configuration in order to make themselves adaptable to ever-changing forces and functional usages. For example, a building could be compactly prepackaged in a factory, and conveniently transported to the site. At the site, it would be energized, causing it to self-deploy or erect itself by means of control systems. Similarly, one can envisage structures which are self-collapsing. reversible, or are able to change shape. or control enclosed space through structural manipulation by means of control devices. The topic addressed in this book. however, belongs·to the first category, namely. controls designed to reduce structural motion. According to Zuk, 3

the earliest attempts in this direction were made in the 1960s when Eugene Freyssinet proposed in 1960 to use prestressing tendons as control devices to stabilize tall structures. Independently, Lev Zetlin in 1965 conceived the idea of designing tall buildings, whereby cables arc 5xed to the structural frame and attached to hydraulic jacks at the base. Sensors are used to detect movement at the top of the structure and to signal a control device which, in turn, directs the action of the jacks. Unfortunately. neither structure was built Other early attempts include that of Kobori and Minai," who advocated the concept of 'dynamic intelligent buildings' capable of executing active response control when they arc subjected to severe earthquakes. Nordell' also suggested the use of active systems which can be activated to provide increased strength to a structure prior to any ·exceptional' overloading. Two examples of such systems are ,sketched in Figs 2.1 and 2.2, A movable diagonal bracing system is shown in Fig, 2. I, In its active state, the diagonal bradngs would increase the lateral resistance of the structure in resisting

exceptional loadings. As it was conceived, the bracing scheme would be manually activated. Similar concepts for movable columns, walls or trusses could also be envisaged aad Fig. 2.2 provides such an example. The columns in their active state would increase both the lateral and vertical resistance. 5

Active structural control: theory und prntticc

1/1(

.{'VV,

'----------'

~

I'

inactive

Hinged bar bracing system 5

Figure 2.1

A systematic assault on active control research did not begin until 1972, when Yao laid down a more rigorous control-theory based concept of sfrtidural ciJntrol. 6 fn this an excessiveCres]Jonse triggered structural control system is suggested as an alternative approach to addressing the safety problem in structural engineering. As described by Yao and in most of the subsequent research and development work, an active structural control system has the basic configuration as shown schematically in Fig. 2.3. It consists of: Sensors located about the structure to measure either external excitations, or structural response variables, or both.

,___

I

..

I -.-.

.Inact~e

Active

I

.. . ··-

;;A Figure 2,2

6

/,;:'(t), the state-space form of Eq. (3.28) is i(t) = Az(t) + bu(t) + hx 0 (t),

z(O) = 0

where

A= [

0'

-wo

b= [

4k~cosa] Ill

and

Under the quadratic performance criterion, the actuator displacement u(t) is to be found such that the integral J given by Eq. (3.7) is minimized. For simplicity, we shall use

Q=[~ ~]

and

where k is structural stiffness as seen in Fig. 3.2(b). The coefficient fJ determines the relative importance of control effectiveness (response reduction) and economy (control force requirements). When fJ < l, control effectiveness is weighted more heavily and, when fJ > 1, economy is more important. They are equally important when fJ = 1. fJ = w represents the uncontrolled case. Let the system parameters take values as those given in Table 3.1. The computed control parameters and control effect on the structural behaviour are summarized in Table 3.2. It is seen that, as discussed earlier, substantial structural modification takes place as reflected by the changes in the natural frequency and the damping factor. In this case, there is a minor change in Table 3.1 System parameter values in Example 3.1 Mass Structure stiffness Tendon stiffness Tendon angle Natural frequency Damping factor

m = 16.69lb-sec 2 /in k = 7934 1b/in k, = 2124 lb/in 36'

"=

'=

w0 =

3.47 Hz 1.24%

17

Aclh'e structurul control: theory und pmcticc

Control parameters and controlled system behaviour

Table 3.2

(1 = :n

Parameter

[1926 16.15

Riccati matrix P Natural frequency (Hz) Damping factor(%)

fJ=l

[1~5

3.47 1.24

16.15

3.780

J

3.58

14.51 ] 1.660

[1035 14.51

3.96 34.0

17.8

natural frequency from uncontrolled to the controlled cases. The damping factor, however, is substantially increased from 1.25% in the uncontrolled case (/1 = co) to 34.0% in one of the controlled cases (/1 = 1). This is also demonstrated graphically in Fig. 3.3 by observing the change in magnitude of the input-output transfer function, the input being x0 (t) and the output x(tJ.

Consider the case in which x0 (t) is a sample of a nonstationary stochastic process resembling an earthquake record as shown in Fig. 3.4. Numerical .·calculations can be carried out to determine the response behaviour of the structure under uncontrolled as well as controlled conditions. The control effect in the time domain can be observed in Figs 3.5-3.7. Figure 3.5 shows reduction in the relative displacement for {1 = 5 and {1 = 1. As indicated earlier, a larger reduction is achieved for a smaller value of {1 as more weight is assigned to the control effectiveness. Corresponding reduction in the absolute acceleration is shown in Fig. 3.6. Figure 3.7 shows the required control force in the tendon which is obtained by multiplying tendon displacement 11(1) by tendon stiffness k,. As expected, larger control forces are required for smaller values of fl. 40

30

10

0 Figure 3,3

18

2

Magnitude of transfer function

4 w (Hz) Hx~(w)

6

8

Control algorithms 0,!

t(sec} Figure 3.4

Base acceleration ln Example 3.1

Example 3.2 Most of the environmental loads, such as wind and earthquakes, to which civil engineering structures are subjected are random in nature. Hence, the analysis of the behaviour of an actively controlled as well as an uncontrolled structure is based on the theory of random vibrations. We shall use this example to demonstrate some steps involved in such an analysis. Also, by using a two-degree-of-freedom structural system, relative merits of several different control configurations can be examined in an elementary way. This example is taken from Yang.' The reader is referred to Appendix A for a review of some basic principles in random vibration analysis. Consider a two-storey building as shown in Fig. 3,8, which is again excited by an earthquake-type ground acceleration X 0 (r). In this example, X 0 (r) is modelled by a nonstationary Gaussian shot noise with X aUl = l/J(r) W(t)

(3.29)

in which W(t) is a stationary zero-mean Gaussian white noise and 1/J(t) is a deterministic modulating function of the form

19

Active structural control: theory and prucrice

if

0.1

~

"

r (sec}

Figure 3.6

20

Relative displacement in Example 3.1 4

Control algorithms

~=5

70 t(